Re: Review of Mueckenheims book.

On Feb 28, 9:46 am, mueck...@xxxxxxxxxxxxxxxxx wrote:
On 26 Feb., 20:22, "MoeBlee" <jazzm...@xxxxxxxxxxx> wrote:

On Feb 24, 4:53 am, mueck...@xxxxxxxxxxxxxxxxx wrote:

On 23 Feb., 20:35, Virgil <vir...@xxxxxxxxxxx> wrote:

In article <1172220975.123624.192...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,

mueck...@xxxxxxxxxxxxxxxxx wrote:
On 22 Feb., 19:30, "MoeBlee" <jazzm...@xxxxxxxxxxx> wrote:
On Feb 22, 5:08 am, mueck...@xxxxxxxxxxxxxxxxx wrote:

And if there is a model of ZFC without this identity function, then
this raises the question, whether this identity function is in other
models. Every set theorist believes that the identity mapping of R
exists in current mathematics - perhaps without reason?

In any set theory in which functions can be defined at all, identity
functions are trivially defineable.

But the function from the inductive set to its power set is not always
among them?

The identity function on omega
(which is a function from omega into
the power set of omega) exists.

The identity function on omega is an automorphism of omega, a function
onto omega.

Yes, since any identity function preserves structure, it is an
automorphism, and the identity function on omega is from omega onto
omega.

And what I wrote is also correct: The identity function on omega is
from omega into the power set of omega.

I have no idea why you would think
this is a matter in question.

If the identity function of every set exists, then the identity
function of P(omega) should exist too. But the different cardinality
of both functions, on omega and on P(omega) cannot be determined?

What are you talking about? The cardinality of any identity function
is the cardinality of the set that the identity function is on.

It
must be a very artificial construction.

AxE!yAz(zey <-> Enex z = <n n>) is a theorem. Why you think that is
any more "artificial" than any other theorem, I don't know.

MoeBlee

.

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